San José State University : Department of Mathematics : Course Descriptions

Course Descriptions

Mathematics Course Descriptions

003A | 003B | 003R | 006A | 006B | 006D | 006L | 008 | 010 | 012 | 019 | 019W | 030 | 030P | 030W | 031 | 031W | 032 | 042 | 050 | 070 | 071 | 100W | 101 | 104 | 105 | 106 | 107A | 107B | 108 | 109 | 110L | 112 | 113 | 115 | 123 | 126 | 128A | 128B | 129A | 129B | 131A | 131B | 132 | 133A | 133B | 134 | 138 | 142 | 143C | 143M | 161A | 161B | 162 | 163 | 164 | 167 | 171 | 175 | 177 | 178 | 179 | 180 | 180H | 201A | 201B | 203 | 211A | 211B | 213 | 221A | 221B | 226 | 229 | 231A | 231B | 233A | 233B | 234 | 235 | 238 | 243A | 243B | 261A | 261B | 265 | 266 | 271A | 271B | 275 | 279A | 279B | 285 | 298 | 299

Important Disclaimer:

Please consult your instructor or the Spartan Bookstore before purchasing textbooks, to make sure you are purchasing the correct textbook and correct edition. Textbooks listed below are only possible texts to give you a feel for the course level and material; the actual textbook used may vary from term to term.

Also, the material in a course during any given semester may vary from what is listed here. You are responsible for obtaining a greensheet from your professor and understanding his/her expectations for the course. The information on this page is to be used for planning/guidance purposes only.

Math 003A: Intensive Learning Mathematics I

Prerequisites: A score of 30 or less on the ELM exam.
Credit: 4 credits, no credit towards graduation
Recent Texts: A Review of Algebra Skills for College Students (McClory)
Background and Goals: A first course in a two semester sequence of courses designed to review topics from elementary and intermediate algebra. Completion of 8 units of Math 003A and Math 003B with a credit grade indicates satisfaction of the ELM requirement.

Math 003B: Intensive Learning Mathematics II

Prerequisites: A credit (CR) grade in Math 003A
Credit: 4 credits, no credit towards graduation
Recent Texts: A Review of Algebra Skills for College Students (McClory)
Background and Goals: The second course in a two semester sequence of courses designed to review topics from elementary and intermediate algebra. Completion of 8 units of Math 003A and Math 003B with a credit grade indicates satisfaction of the ELM requirement.

Math 003R: Entry Level Mathematics Review

Prerequisites: A grade of NC in Math 3A (Intensive Learning Mathematics I) or Math 6A (Entry Level Mathematics I).
Frequency: Spring
Credit: 5 credits, no credit for graduation.
Recent Texts: A Review of Algebra Skills for College Students (McClory)
Background and Goals: Review of topics from elementary and intermediate algebra. Completion of 003R with a credit grade indicates satisfaction of the ELM requirement.

Math 006A: Entry Level Mathematics I

Prerequisites: A score between 32 and 40 on the ELM exam.
Frequency: Fall
Credit: 3 credits, no credit for graduation.
Recent Texts: A Review of Algebra Skills for College Students (McClory)
Background and Goals: A first course in a two semester sequence of courses designed to review topics from elementary and intermediate algebra.

Math 006B: Entry Level Mathematics II

Prerequisites: A credit (CR) grade in Math 006A.
Frequency: Spring
Credit: 3 credits, no credit for graduation.
Recent Texts: A Review of Algebra Skills for College Students (McClory)
Background and Goals: A second course in a two semester sequence of courses designed to review topics from elementary and intermediate algebra.

Math 006D: Entry Level Mathematics

Prerequisites: A score of 46 or 48 on the ELM exam and permission of the Developmental Math Coordinator.
Frequency: Fall, Spring
Credit: 5 credits, no credit for graduation.
Recent Texts: A Review of Algebra Skills for College Students (McClory)
Background and Goals: A review of topics from elementary and intermediate algebra.

Math 006L: Entry Level Mathematics

Prerequisites: A score between 42 and 48 on the ELM exam.
Credit: 5 credits, no credit for graduation.
Recent Texts: A Review of Algebra Skills for College Students (McClory)
Background and Goals:

Math 008: College Algebra

Prerequisites: Satisfaction of ELM requirement.
Frequency: Every semester
Credit: 3 credits, satisfies GE area B4.
Recent Texts: College Algebra and Trigonometry (Dugopolski).
Background and Goals: To understand functions and be able to graph elementary functions, specifically polynomial and trigonometric functions. To be able to find the inverse of a function. In trigonometry, it is important that a student learn the trigonometric functions, their inverses and graphs. Deriving one identity from another, laws of sines and cosines. Applications are important whenever possible.
Content: Topics in College Algebra. Trigonometric functions, trigonometric identities, solution of trigonometric equations and applications of trigonometry.

Math 010: Mathematics for General Education

Prerequisites: Satisfaction of the ELM requirement.
Frequency: Every semester
Credit: 3 credits, may be used to satisfy the GE Area B4.
Recent Texts: Using and Understanding Mathematics (Bennett and Briggs).
Background and Goals: The major goal is to enable the student to use numerical and graphical data in personal and professional judgments and in coping with public issues. More specifically, a mathematical concepts course should prepare the student to use mathematical methods to solve quantitative problems, including those presented in verbal form; demonstrate the ability to use mathematics to solve real life problems; and arrive at conclusions based on numerical and graphical data.
Content: Topics from: methods of proof, problem solving, trigonometry, probability, statistics, applications to scheduling and apportionment, population studies, consumer math, theory of games, polyhedra, networks, graph theory, linear programming.

Math 012: Number Systems

Prerequisites: Two years of high school algebra, one year of high school geometry, and satisfaction of ELM requirement.
Frequency: Every semester
Credit: 3 credits
Recent Texts: Mathematics for Elementary School Teachers (Musser, Burger, & Peterson).
Background and Goals: This is a first course in a three course sequence (012, 105, 106) for elementary and middle school teachers. Students explore and develop understanding of mathematical concepts and processes taught at those levels. In particular, students study problem solving techniques, numeration systems, the structure of the real number system, and elementary number theory. Throughout the course, students experience mathematics learning in the way that we want their future students to experience mathematics learning. In addition, students analyze their learning experiences from the perspective of a future teacher. Technology is integrated as appropriate.
Content: Structure of the real number system, numeration systems, elementary number theory, and problem-solving techniques; technology integrated throughout the course.

Math 019: Precalculus

Prerequisites: Satisfaction of ELM requirement. Concurrent enrollment in MATH 19W Precalculus Workshop required.
Frequency: Every semester
Credit: 5 credts, counts towards GE area B4.
Recent Texts: Precalculus Mathematics for Calculus (Stewart, Redlin and Watson).
Background and Goals: The primary goal in this course is to prepare students for calculus. Students are expected to master skills required to perform algebraic manipulations. They must understand functions and be able to apply the basic ideas relating to functions: domain, range, graphs, asymptotes, zeros, and operations on functions. They are expected to understand characteristics and special properties of polynomial, rational, exponential, logarithmic, trigonometric, and inverse trigonometric functions, conic sections, and analytic geometry.
Content: Preparation for calculus: polynomial, rational, exponential, logarithmic and trigonometric functions; analytic geometry.

Math 019W: Precalculus Workshop

Prerequisites: Concurrent Enrollment in Math 019 (Precalculus).
Frequency: Every semester
Credit: 1 credit.
Background and Goals: A course designed to help all students excel in Math 19. Students work in groups on challenging problems to help them understand precalculus concepts more deeply and lay the groundwork for success in future math courses.
Content: Preparation for Calculus: polynomial, rational, exponential, logarithmic and trigonometric functions; analytic geometry.

Math 030: Calculus I

Prerequisites: Satisfaction of ELM requirement; Satisfactory score on the Mathematics Placement Exam, or MATH 19 or MATH 19A (with a grade of "B" or better to waive the placement exam).
Frequency: Every semester.
Credit: 3 credits
Recent Texts: Calculus, Early Transcendentals (Stewart).
Background and Goals: To learn the concepts and techniques of differential calculus and use them in solving applied problems. To study limits, continuity, differentiation and applications of the derivative, including related rates and optimization problems.
Content: Introduction to calculus including limits, continuity, differentiation, applications and introduction to integration. Graphical, algebraic and numerical methods of solving problems.

Math 030P: Calculus I with Precalculus

Prerequisites: Satisfactory score on the calculus placement exam or Math 19 (with a grade of C– or better); satisfaction of the ELM requirement.
Frequency: Every semester
Credit: 5 credits
Recent Texts: Calculus, Early Transcendentals (Stewart)
Background and Goals: To review selected topics in precalculus. To learn the concepts and techniques of differential calculus and use them in solving applied problems. To study limits, continuity, differentiation and applications of the derivative.
Content: Selected topics in Precalculus. Introduction to Calculus including limits, continuity, differentiation, applications and introduction to integration. Graphical, algebraic and numerical methods of solving problems.

Math 030W: Calculus I Workshop

Prerequisites: Concurrent enrollment in Math 030 (Calculus I) or Math 030P (Calculus I with Precalculus).
Frequency: Every semester
Credit: 1 credit
Recent Texts: Calculus, Early Transcendentals (Stewart)
Background and Goals: A course designed to help all students excel in Calculus I.
Content: Students work in groups on challenging calculus problems to help them understand the concepts in Calculus I more deeply and lay the groundwork for success in future math courses.

Math 031: Calculus II

Prerequisites: Math 030 (Calculus I) with a grade of C- or higher.
Frequency: Every semester.
Credit: 4 credits
Recent Texts: Calculus, Early Transcendentals (Stewart)
Background and Goals: To learn the concepts and techniques of integral calculus and to use them in solving applied problems. To learn the concept of infinite sequences and series. To investigate convergence properties of numerical and power series and their application to representation of functions as power series.
Content: Definite and indefinite integration with applications. Sequences and series. Graphical, algebraic and numerical methods of solving problems.

Math 031W: Calculus II Workshop

Prerequisites: Concurrent enrollment in Math 031 (Calculus II)
Frequency: Every semester
Credit: 1 credit
Recent Texts: Calculus, Early Transcendentals (Stewart)
Background and Goals: A course designed to help all students excel in Calculus II.
Content: Students work in groups on challenging calculus problems to help them understand the concepts in Calculus II more deeply and lay the groundwork for success in future math courses

Math 032: Calculus III

Prerequisites: Math 031 (Calculus II) with a grade of C- or higher.
Frequency: Every semester
Credit: 3 credits
Recent Texts: Multivariable Calculus, Early Transcendentals (Stewart).
Background and Goals: To learn 2- and 3- dimensional vector algebra and analytic geometry. To understand and apply the basic ideas of multivariable calculus: functions, limits, continuity, differentiation, and integration. To master the concepts and techniques of multivariable calculus and to use these methods in solving applied problems.
Content: Functions of more than one variable, partial derivatives, multiple integrals and vector calculus. Graphical, algebraic and numerical methods of solving problems.

Math 042: Discrete Mathematics

Prerequisites: Math 019 (Precalculus) or equivalent.
Frequency: Every semester.
Credit: 3 credits
Recent Texts: Discrete Mathematics and Its Applications (Rosen).
Background and Goals: To introduce students to mathematical proofs, techniques, and terminology, and to begin developing mathematical sophistication.
Content: Sets, logic, methods of proof including mathematical induction, functions, relations, elementary combinatorics, probability, Boolean algebras.

Math 050: Scientific Computing I

Prerequisites: Math 032 (Calculus III) or instructor's consent
Credit: 2 credits (1 lecture hour, 3 lab hours per week)
Content: Computer systems and programming, emphasizing solution of problems in atmospheric sciences. Includes computer systems, flow diagrams, UNIX and C FORTRAN programming, mass data handling and formatting.

Math 070: Finite Mathematics

Prerequisites: Satisfication of the ELM requirement.
Frequency: Every semester
Credit: 3 credits, counts toward GE area B4.
Recent Texts: Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences (Barnett, Ziegler, Byleen).
Background and Goals: To learn counting principles, permutations, combinations, probability, probability distribution, expectation, conditional probability, Bayes’ formula, matrices, and their applications, solving systems of linear equations and linear inequalities, linear programming, computing interest, present and future value of annuities.
Content: Systems of linear equations and inequalities, matrices, linear programming, set theory and probability theory, applications to business and to social sciences.

Math 071: Calculus for Business and Aviation

Prerequisites: Satisfaction of ELM requirement.
Frequency: Every semester
Credit: 3 credits
Recent Texts: Calculus for Business, Economics, Life Sciences, and Social Sciences(Barnett, Ziegler, Byleen).
Background and Goals:
Content: Functions and graphs, limits, continuity, differentiation, integration, partial differentiation. Emphasis on business and economics applications.

Math 100W: Technical Writing Workshop

Prerequisites: ENGL 1B (with a grade of "C" or better); Completion of core GE; satisfaction of Writing Skills Test; upper division standing
Frequency: Every semester
Credit: 3 credits, GE Area Z
Content: Advanced writing through preparation of technical reports and presentations. Improving skills for writing subject-related reports, project proposals and personal resumes through practice and evaluation. Course assignments will be related to issues concerning careers in mathematics and mathematics education.

Math 101: Problem Solving for Teachers

Prerequisites: Math 106 with grade of C- or better, or instructor's consent.
Frequency: Every other semester (Spring)
Credit: 3 credits
Content: Problem solving involving elementary number theory, algebra, geometry, logic, measurement, probability and statistics. Selected problems explored and extended across content strands. Various instructional methods and assessment alternatives modeled. Designed specifically for teachers of mathematics, grades K-8.

Math 104: History of Mathematics

Prerequisites: Math 042 (Discrete Math) and Math 115 (Modern Geometry and Transformations)
Frequency: Every other semester (Fall)
Credit: 3 credits
Recent Texts: An Introduction to the History of Mathematics (Eve)
Content: Mathematical development from earliest times to the twentieth century.

Math 105: Concepts in Mathematics, Probability and Statistics

Prerequisites: Math 012 (Number Systems) with a grade of C- or higher.
Frequency: Every semester
Credit: 3 credits.
Recent Texts: Mathematics for Elementary School Teachers (Musser, Burger, & Peterson)
Background and Goals: Mathematics 105 is the second course in a three-course sequence designed for prospective elementary and middle school teachers. Students explore and develop understanding of mathematical concepts and processes taught at those levels. In particular, students study problem-solving techniques, functions and algebraic reasoning, ratio and proportions, probability, data, graphs, and statistics. Throughout the course, students experience mathematics learning in the way that we want their future students to experience mathematics learning. In addition, students analyze their learning experiences from the perspective of a future teacher. Technology is integrated throughout the course.
Content: Introduction to functions and algebraic reasoning, introduction to probability, data, graphs, statistics, problem solving; technology integrated throughout the course.

Math 106: Intuitive Geometry

Prerequisites: Math 105 (Concepts in Mathematics, Probability and Statistics) and Math 012 (Number Systems) with grade of C- or higher.
Frequency: Every semester
Credit: 3 credits
Recent Texts: Mathematics for Elementary School Teachers (Musser, Burger, & Peterson)
Background and Goals: Mathematics 106 is the third course designed for prospective elementary and middle school teachers. Students explore and develop understanding of mathematical concepts and processes taught at those levels. In particular, students study two- and three-dimensional geometric objects; analyze characteristics and properties of two- and three-dimensional geometric shapes; develop mathematical arguments about geometric relationships; apply transformations and use symmetry to analyze mathematical situations; represent geometric objects using representational systems such as concrete models, drawings and coordinate geometry; and use techniques, tools and formulas for determining measurements.
Content: Introductory geometry, measurement, inductive and deductive reasoning, introduction to transformations, and problem-solving techniques; technology integrated throughout the course.

Math 107A: Explorations in Algebra

Prerequisites: Math 106 (Intuitive Geometry) or instructor's consent.
Frequency: Every other semester (Fall)
Credit: 3 credits
Content: Comprehensive view of school algebra primarily for the mathematical preparation of teachers. The computer will be used togenerate examples, investigate relationships, explore algorithms and solve problems. Functions and relations used as a unifying theme throughout.

Math 107B: Explorations in Geometry

Prerequisites: Math 106 (Intuitive Geometry) with grade of C- or higher, or instructor's consent.
Frequency: Every other semester (Spring)
Credit: 3 credits
Recent Texts: Geometry: An Investigative Approach (O’Daffer and Clemens)
Content: Comprehensive view of elementary geometry primarily for the mathematical preparation of teachers. The computer will be used to investigate two- and three-dimensional patterns, measurement and parallelism. Transformational approach to congruence and similarity. Nature of inductive reasoning and deductive proof.

Math 108: Introduction to Abstract Mathematics and Proofs

Prerequisites: Math 031 (Calculus II) and Math 042 (Discrete Mathematics) with grade of C- or higher.
Frequency: Every semester.
Credit: 3 credits
Recent Texts: Mathematical Thinking: Problem Solving and Proofs (D’Angelo and West), Introduction to Advanced Mathematics (Barnier and Feldman)
Background and Goals: To learn what constitutes a valid argument and to be able to utilize a variety of proof styles to give valid proofs and disproofs.
Content: The purpose of this course is to develop students' mathematical maturity and skill with proofs. Material covered will include logic; set theory including functions, relations, and cardinality; the real number system, including the completeness axiom; and selected topics.

Math 109: Mathematical Software

Prerequisites: Math 032 (Calculus III) and either Math 123 (Differential Equations and Linear Algebra) or Math 129A (Linear Algebra), with grade of C- or higher.
Frequency: Every other semester (Fall)
Credit: 3 credits
Content: Use of mathematical software in selected fields of mathematics such as calculus, multivariable calculus, differential equations, combinatorics, statistics, and linear algebra. A programming project will be required.

Math 110L: Mathematics Computing Laboratory

Prerequisites: Concurrent enrollment in any mathematics course and instructor's consent.
Frequency: Every semester
Credit: 1 credit (credit/no credit grading basis), does not count towards major/minor requirements
Content: Programming projects related to mathematics courses. Required for use of department labs.

Math 112: Vector Calculus

Prerequisites: Math 032 (Calculus III) with grade of C- or better
Frequency: Almost every semester (except Fall even years).
Credit: 3 credits.
Recent Texts: Vector Calculus (P.C. Matthews), Inroduction to Vector Analysis (Davis & Snyder), Div, grad, curl and all that (H.M. Schey).
Background and Goals: This course is a continuation of math 032, covering vector calculus in R² and R³ and its applications to science and engineering. This course focuses on concepts and computation rather than proof, with selected applications of the theory to such fields as mechanics, astrodynamics, electromagnetism, fluid mechanics, aerodynamics, and gas dynamics.
Content: Vector fields, line and surface integrals, Green’s Theorem, Stokes’ Theorem, Divergence Theorem and advanced topics such as differential forms or applications to mechanics, fluid mechanics, or electromagnetism.

Math 113: Differential Geometry

Prerequisites: Math 032 (Calculus III) and Math 129A (Linear Algebra) with grade of C- or higher
Frequency: Alternate years (Spring, even years)
Credit: 3 credits
Recent Texts: Elementary Differential Geometry (O’Neil), Elements of Differential Geometry (Milman and Parker).
Background and Goals:
Content: Properties of curves and surfaces, Frenet-Serret formulas and the fundamental forms. Study of curves and surfaces in the small by means of differential calculus.

Math 115: Modern Geometry and Transformations

Prerequisites: Math 031 (Calculus II) with grade of C- or higher.
Frequency: Almost every semester (except Spring, odd years
Credit: 3 credits
Recent Texts: Modern Geometries (Smart)
Background and Goals:
Content: Synthetic and analytic theory of projective transformations, similarities, Euclidian motions, inversive geometry and an introduction to non-Euclidean geometry.

Math 123: Differential Equations and Linear Algebra

Prerequisites: Math 031 (Calculus II) with grade of C- or higher.
Frequency: Every semester
Credit: 3 credits
Content: Matrices, determinants, systems of linear equations, vector geometry, linear transformations, eigenvalues and eigenvectors, diagonalization, first order differential equations, linear systems of differential equations, higher order differential equations, Laplace transforms.

Math 126: Theory of Numbers

Prerequisites: Math 031 (Calculus II) and Math 042 (Discrete Math) with grade of C- or higher.
Frequency: Every other semester (Fall)
Credit: 3 credits
Recent Texts: Elements of the Theory of Numbers (Dence and Dence), Elementary Introduction to Number Theory (Long), Elementary Number Theory (Vanden Eynden), A Friendly Introduction to Number Theory (Silverman)
Content: Divisibility, prime numbers, congruences of first and higher degrees, theorems of Fermat, Euler and Wilson, Quadratic residues.
Subsequent Courses: Math 226 (Theory of Numbers)

Math 128A: Abstract Algebra I

Prerequisites: Math 108 (Introduction to Proofs) and Math 129A (Linear Algebra I), with grades of C- or higher, or instructor's consent.
Frequency: Almost every semester (except Spring, even years)
Credit: 3 credits
Recent Texts: A First Course in Abstract Algebra (Fraleigh, Addison Wesley), Abstract Algebra: An Introduction (Hungerford, Harcourt), Contemporary Abstract Algebra (Gallian).
Background and Goals:
Content: Group theory: permutation groups, abelian groups, morphism theorems, finite groups. Introduction to rings and fields.

Math 128B: Abstract Algebra II

Prerequisites: Math 128A (Abstract Algebra I) with grade of C- or higher.
Frequency: Every other semester (Spring)
Credit: 3 credits
Recent Texts: A First Course in Abstract Algebra (Fraleigh, Addison Wesley), Abstract Algebra: An Introduction (Hungerford, Harcourt), ContemporaryAbstract Algebra (Gallian).
Content: Emphasis on rings, integral domains, fields, field extensions, Galois theory.

Math 129A: Linear Algebra I

Prerequisites: Math 031 (Calculus II) with grade of C- or higher.
Frequency: Every semester
Credit: 3 credits
Recent Texts: Linear Algebra and Its Applications (Lay), Elementary Linear Algebra (Spence, Insel, and Friedberg), Linear Algebra With Applications (Bretscher).
Background and Goals: To provide students with working knowledge of vectors and matrices, examples of linear algebra application, and experience of using software to solve linear algebra problems.
Content: Matrices, systems of linear equations, vector geometry, matrix transformations, determinants, eigenvectors and eigenvalues, orthogonality, diagonalization, applications, computer exercises. Theory in Rⁿ emphasized; general real vector spaces and linear transformations introduced.

Math 129B: Linear Algebra II

Prerequisites: Math 108 (Introduction to Proofs) and an introduction to matrices such as Math 129A (Linear Algebra I) with grade of C- or higher.
Frequency: Almost every semester (except Fall, even years)
Credit: 3 credits
Recent Texts: Linear Algebra (Friedberg, Insel, and Spence)
Background and Goals: Students should master the language of vector spaces and linear maps, and gain solid understanding of the structure of linear maps on finite dimensional spaces.
Content: Continuation of Math 129A. Abstract vector spaces and linear transformations, diagonalization, Cayley-Hamilton theorem, minimal polynomials, Jordan canonical form. Selected topics from inner product and adjoint, duality, rational canonical form and applications.

Math 131A: Introduction to Analysis

Prerequisites: Math 032 (Calculus III) and Math 108 (Introduction to Proofs) with grade of C- or higher.
Frequency: Almost every semester (except Fall, odd years)
Credit: 3 credits
Recent Texts: Elementary Analysis: The Theory of Calculus (Ross), Introduction to Real Analysis (Bartle and Sherbert)
Background and Goals:
Content: Properties of real numbers including completeness and compactness. Continuous functions, uniform continuity, the derivative.

Math 131B: Introduction to Real Variables

Prerequisites: Math 131A (Introduction to Analysis) with grade of C- or higher.
Frequency: Every other semester (Fall)
Credit: 3 credits
Recent Texts: Introduction to Real Analysis (Bartle and Sherbert)
Background and Goals:
Content: The theory of the Riemann integral, sequences and series of functions, spaces of functions.

Math 132: Advanced Calculus

Prerequisites: Math 032 (Calculus III) and Math 129A (Linear Algebra) with grades of C- or better.
Frequency: Every other semester (Fall)
Credit: 3 credits.
Recent Texts: Functions of Several Variables(Fleming), Advanced Calculus of Several Variables (C.H. Edwards), Multivariable Mathematics (Shifrin), or Analysis on Manifolds (Munkres).
Background and Goals: This course develops multivariable Calculus and elementary function theory at a more rigorous level than encountered in math 032, focusing on the generalization to function from Rⁿ to R^m. The emphasis is on concepts and applications, but arguments will be rigorous.
Content: Calculus of several variables, Jacobian, inverse and implicit function theorems, contraction mapping theorem, change of variables in integration and applications.

Math 133A: Ordinary Differential Equations

Prerequisites: Math 032 (Calculus III) with grade of C- or higher.
Frequency: Every semester
Credit: 3 credits
Recent Texts: Elementary Differential Equations (Boyce and Diprima), Ordinary Differential Equations (Blanchard, Devaney, Hall)
Background and Goals: The objective of this course is for students to gain an understanding of ordinary differential equations, solutions, and applications to science and engineering while increasing their problem solving abilities through word problems and projects and enhancing their critical thinking skills.
Content: First order differential equations, first order linear systems, second order linear equations, applications, Laplace transforms, series solutions. Additional topics.

Math 133B: Partial Differential Equations

Prerequisites: Math 133A (Ordinary Differential Equations) with grade of C- or higher.
Frequency: Almost every semester (except Fall, odd years)
Credit: 3 credits
Recent Texts: Partial Differential Equations with Fourier Series and Boundary Value Problems (Asmar), Applied Differential Equations With Fourier Series and Boundary Value Problems (Haberman)
Background and Goals: To gain an understand of the partial differential equations of applied mathematics in 1, 2 and 3 dimensions, and their solutions in special geometries (cartesian, cylindrical, and spherical).
Content: Partial differential equations of physics and engineering (such as the heat and wave equations), Fourier series, Legendre polynomials, Bessel functions, orthogonal functions, the Sturm-Liouville equation, Method of Characteristics, and additional topics.

Math 134: Dynamical Systems

Prerequisites: Math 129A (Linear Algebra) and Math 133A (Ordinary Differential Equations) with grades of C- or better.
Frequency: Alternating years (Spring, odd years)
Credit: 3 credits.
Recent Texts: Differential Equations, Dynamical Systems, and an Introductions to Chaos (Hirsch, Smale, and Devaney), Nonlinear Dynamics and Chaos (Strogatz), Dynamics and Bifurcations (Hale and Kocak).
Background and Goals: The goal is to gain an understanding of the qualitative theory of dynamical systems and their applications to physics and engineering. The focus may be on planar nonlinear systems, bifurcation theory, chaos, or possibly discrete dynamical systems.
Content: Introduction to dynamical systems theory and its applications. Topics include dynamical systems defined by maps and ordinary differential equations, stability, bifurcation theory, invariant manifolds and attractors. Applications will be taken from the physical sciences and engineering.

Math 138: Complex Variables

Prerequisites: Math 032 (Calculus III) with grade C- or higher.
Frequency: Every other semester (Spring)
Credit: 3 credits.
Recent Texts: Complex Variables With Applications (Churchill and Brown).
Background and Goals: To learn all possible operations on the complex numbers, understand functions of a complex variable, limits and continuity. To understand analytic functions, the Cauchy-Riemann equations, harmonic functions and the connection between complex variables and applied mathematics problems. To master the elementary complex functions and their properties. To learn the meaning of a contour integral and the well-known results such as the cauchy theorem, Cauchy integral formula, the residue theorem. To understand the convergence of power series and Laurent series, and to be able to compute real definite integrals by using residues.
Content: Complex numbers, analytic functions, Cauchy-Riemann equations, contour integration, Taylor and Laurent series, Residue Theory, Conformal Mappings and applications to physical sciences.

Math 142: Introduction to Combinatorics

Prerequisites: Math 031 (Calculus II) and Math 042 (Discrete Math), with grades of C- or better.
Frequency: Almost every semester (except Spring, odd years)
Credit: 3 credits
Recent Texts: Applied Combinatorics with Problem Solving (Jackson and Thoro), Applied Combinatorics (Tucker).
Background and Goals:
Content: Sets, permutation, combinations, probability, counting techniques, generation functions, partitions, recurrence relations, inclusion-exclusion. Polya’s theorem and applications to computer science, mathematics engineering, physical sciences.

Math 143C: Numerical Analysis and Scientific Computing

Prerequisites: Math 32 (Calculus III); one of CS 50, CS 46A or CS 49 (with a grade of "C-" or better in each) or instructor consent.
Frequency: Every other semester (Spring)
Credit: 3 credits
Recent Texts: Numerical Analysis (Burden and Faires)
Background and Goals:
Content: Development and comparison of important algorithms for scientific computing in terms of efficiency, accuracy and reliability. Topics include nonlinear equations, interpolation, approximation theory, differentiation, integration, differential equations, numerical stability and error analysis. Substantial assignments using contemporary software packages and professional subprogram libraries.

Math 143M: Numerical Analysis and Scientific Computing

Prerequisites: Math 129A (Linear Algebra I) and one of CS 50, CS 46A or CS 49 (with a grade of "C-" or better in each) or instructor consent.
Frequency: Every other semester (Fall)
Credit: 3 credits
Recent Texts: Fundamentals of Matrix Computations (David Watkins)
Background and Goals:
Content: Development and comparison of important algorithms for scientific computing in terms of efficiency, accuracy and reliability. Topics include systems of linear equations-direct and iterative methods, least squares problems, eigenvalues and eigenvectors, numerical stability and error analysis. Substantial assignments using contemporary software packages and professional subprogram libraries.

Math 161A: Applied Statistics I

Prerequisites: Math 031 (Calculus II) with grade of C- or higher.
Frequency: Every semester
Credit: 3 credits
Recent Texts: Probability and Statistics for Engineering and the Sciences (Devore)
Background and Goals: To enable the student to begin to think statistically and to perform basic statistical analyses. The student should begin to view a data set as the output of a random experiment and thus as coming from some underlying probability distribution and should learn to make valid inferences from the data.
Content: Descriptive and inferential statistics. Collection and analysis of data, discrete and continuous probability models, random variables, Central Limit Theorem, confidence intervals, hypothesis testing.

Math 161B: Applied Statistics II

Prerequisites: Math 161A (Applied Statistics I) with grade of C- or higher.
Frequency: Almost every semester (except Spring, even years)
Credit: 3 credits
Recent Texts: Probability and Statistics for Engineering and the Sciences (Devore)
Background and Goals: Review of hypothesis testing from Applied Statistics I, Math 161A. Introduction of two-sample tests. Analysis of variance for one-factor and several-factor experiments. Linear and multiple regression. Use of statistical software is an integral part of the course. The students should work on a (data analysis) project using the methods discussed in the course.
Content: A continuation of Math 161A. Two sample confidence intervals and hypothesis tests, analysis of variance, simple and multiple regression, chi-square tests of homogeneity and goodness-of-fit, other topics as time permits. Use of statistical software is integral to the course. Student project required.

Math 162: Statistics for Bioinformatics

Prerequisites: Math 161A (Applied Statistics I) with grade of C- or higher.
Frequency: Alternating years (Spring, even years)
Credit: 3 credits
Recent Texts:
Background and Goals:
Content: Introduction to the theory and applications of statistical methodology in biological problems. Topics include classification, clustering, prediction, Markov models and experimental design. Emphasis on applying statistical methods to molecular biology problems. No biology background required.

Math 163: Probability Theory

Prerequisites: Math 032 (Calculus III) and Math 161A (Applied Statistics I) with grade of C- or higher
Frequency: Every other semester (Fall)
Credit: 3 credits
Recent Texts: A First Course in Probability (Ross)
Background and Goals: Using the theory of probability, combinatorics, and univariate/multivariate discrete/continuous distributions to model applications. Probability laws, bounds, and limit theorems. Expectations, moment generating functions, and sampling distributions.
Content: Probability axioms; random variables; marginal and conditional density and distribution functions; binomial, geometric, Poisson, gamma and normal probability laws; mathematical expectations, moment generating functions; limit theorems; sampling distributions.

Math 164: Mathematical Statistics

Prerequisites: Math 163 (Probability Theory) with grade of C- or higher.
Frequency: Every other semester (Spring)
Credit: 3 credits
Recent Texts: An Introduction to Mathematical Statistics and Its Applications (Larsen and Marx)
Background and Goals:
Content: Sampling distributions, confidence intervals, order statistics, sufficient statistics, the Rao-Blackwell Theorem, completeness, uniqueness, point estimation, maximum likelihood, Bayes' methods, testing hypotheses, likelihood ratio tests, categorical data analysis, nonparametric tests.

Math 167: Programming in SAS

Prerequisites: Math 161A (Applied Statistics I) with grade of C- or higher
Frequency: Every other semester (Spring)
Credit: 3 credits
Recent Texts:
Background and Goals:
Content: Programming and applying the computer language SAS to perform statistical computations and to analyze large amounts of data. Data preparation and transformations, creating and managing data files, macros, data reporting techniques, basic statistical methods.

Math 171: Foundations of Mathematics and Computer Science

Prerequisites: Math 042 (Discrete Math) and upper division algebra
Frequency: Alternate years (Spring, odd years)
Credit: 3 credits
Recent Texts: A mathematical introduction to logic (Enderton)
Background and Goals: Introduce students to the syntax and semantics of first-order logic. Prove the Completeness and Compactness theorems and provide examples and applications.
Content: Fundamental and unifying principles of logic and computation. Introduction to mathematical logic for the mathematician and computer scientist.

Math 175: Introduction to Topology

Prerequisites: Math 131A (Introduction to Analysis)
Frequency: Alternating years (Fall, odd years)
Credit: 3 credits
Recent Texts: Topology (Munkres)
Background and Goals:
Content: Set theory, topological spaces and separation axioms, completeness, compactness, connectedness, functions and continuity, product spaces.

Math 177: Linear and Non-Linear Optimization

Prerequisites: MATH 129A (Linear Algebra) or instructor consent.
Frequency: Alternating years (Fall, even years)
Credit: 3 credits
Recent Texts: Linear Programming and Game Theory (Thie), Introduction to Mathematical Programming (Winston and Venkataramanan), Optimization in Operations Research (Rardin).
Background and Goals: Teach students to model a variety of problems using linear and nonlinear programming. Introduce the basic algorithms for solving linear and nonlinear optimization problems, and optimization software in a variety of packages. Cover the basic mathematical theory behind the standard algorithms.
Content: Linear inequalities, the simplex method and other algorithms, duality, integer optimization, convex optimization, quadratic optimization, game theory.

Math 178: Mathematical Modeling

Prerequisites: Math 129A (Linear Algebra)
Frequency: Every other semester (Spring)
Credit: 3 credits
Recent Texts:
Background and Goals:
Content: Basic modeling techniques including graphing, proportion, curve fitting and interpolation, optimization, probability and computer simulation, derivatives and differences. Technology will be incorporated to model applied problems from business/economics, physical/life/social sciences and engineering.

Math 179: Introduction to Graph Theory

Prerequisites: Math 042 (Discrete Math) and Math 129A (Linear Algebra)
Frequency: Alternating years (Fall, odd years)
Credit: 3 credits
Recent Texts: Applied and Algorithmic Graph Theory (Chartrand and Oellermann)
Background and Goals: This is a course that covers many of the basic topics in graph theory and some of the standard graph algorithms. Topics to be covered include graph models, isomorphism, connectivity, depth-first search, blocks, cutpoints, distance, breadth-first search, Dijkstra’s algorithm, trees, minimum-weight spanning trees, Prim’s and Kruskal’s algorithms, bipartite graphs, matchings, augmenting paths and matching algorithms, maximum-weight matchings, networks and network flow algorithms, Eulerian circuits and the Chinese postman problem, hamiltonian circuits and the traveling salesman problem, planar graphs and planarity algorithms, graph colorings and chromatic number, etc.
Content: Hamiltonian and Eulerian properties, matching, trees, connectivity, coloring problems and planarity. Emphasis on algorithms and applications, including optimal network flows.

Math 180: Individual Studies

Prerequisites: Instructor consent.
Credit: 1-4 credits, (grading: Credit / No Credit)
Content: Individual study in a specific field.

Math 180H: Individual Studies for Honors

Prerequisites: At least junior standing as mathematics major. GPA of 3.5 or higher in the major and department chair consent.
Credit: 3 credits, (grading: Credit / No Credit)
Content: Senior project on advanced topics in mathematics as determined by the instructor. Written paper and oral presentation of the project required. Intended for students graduating with departmental honors.

Math 201A: Mathematics for Secondary Teachers

Prerequisites: Equivalent of math minor (18 units including 9 upper division units) or instructor consent.
Credit: 3 credits
Recent Texts: Ways to Think About Mathematics (Benson and Addington), The Art of Problem Posing (Brown and Walter).
Background and Goals:
Content: Secondary school mathematics from an advanced viewpoint, plus topics from higher mathematics. Emphasizes inductive reasoning in problem solving. Applications useful to junior and senior high school teachers.

Math 201B: Mathematics for Secondary Teachers

Prerequisites: Equivalent of math minor (18 units including 9 upper division units) or instructor consent.
Recent Texts: Thinking mathematically (Mason, Burton, & Stacey)
Background and Goals:
Content: Secondary school mathematics from an advanced viewpoint, plus topics from higher mathematics. Emphasizes deductive reasoning in problem solving. Applications useful to junior and senior high school teachers.

Math 203: Applied Mathematics, Computation, and Statistics Projects

Prerequisites: Instructor Consent.
Credit: 3 credits (grading: Credit - No Credit)
Recent Texts:
Background and Goals: Supervised teamwork to solve a substantial problem in mathematics or computer science usually supplied by an outside agency such as a local company. The number of different projects offered and the topics will vary widely. A project usually continues for two consecutive semesters.
Content: see CAMCOS webpage for more information.

Math 211A: Geometry of Projective Spaces

Prerequisites: Math 112 (Vector Calculus) or Math 115 (Modern Geometries and Transformations)
Frequency: Alternating years (Spring, odd years).
Credit: 3 credits
Recent Texts: Geometry and Analysis of Projective Spaces (Springer)
Background and Goals: The course is a detailed study of analytic or synthetic projective geometry in one and two dimensions. The study of one dimensional homographies includes homogeneous coordinates, cross ratio, perspectivities and projectivities between point ranges, vanishing points, involutions, invariant points and other invariant properties of binary forms. Major topics in the study of two dimensional homographies are duality, homogeneous point and line coordinates, properties of a homography, cross ratio of points and lines, trilinear coordinates, central projection, Theorem of Desargues, and imaginary elements.
Content: Structure of projective planes; finite planes and combinatorics; automorphism groups; configuration theorems and coordinatizations; conics; introduction to projective n-space over a field; topological properties; subgeometries.

Math 211B: Advanced Topics in Geometry

Prerequisites: Math 211A (Geometry of Projective Spaces)
Frequency: Alternating years (Fall, odd years).
Credit: 3 credits
Recent Texts: Geometry and Analysis of Projective Spaces (Springer)
Background and Goals: The first part of the course is a completion of the study of analytic projective geometry in two dimensions, with emphasis on the conic. The second part is an introduction to analytic projective geometry of three and more dimensions. The study of additional concepts in two dimensions includes collineations and correlations between two planes and of a plane onto itself, geometric and algebraic classifications of collineations, and special cases of collineations. The work on the conic involves projective definitions, poles and polars, polar reciprocation, Theorem of Pascal, pencil of conics, and invariants of pencil of conics. The non-Euclidean section includes analytic elliptic and hyperbolic geometries, along with the significance of non-Euclidean geometries. The final section includes linear spaces, projectively related spaces, and perspectivities in 3 dimensions, the quadric, line coordinates, and affine and in 3 dimensions, the quadric, line coordinates, and affine and in 3 dimensions, the quadric, and line coordinates, and affine and Euclidean specializations.
Content: Projective n-space, linear geometry, crystallography, algebraic geometry and additional topics.

Math 213: Advanced Differential Geometry

Prerequisites: Math 113 (Differential Geometry)
Frequency: Alternating years (Fall, even years).
Student Body: Math graduate students in pure and applied mathematics.
Credit: 3 credits.
Background and Goals: An intensive study of the intrinsic geometry of surfaces and of Riemannian geometry.
Content: Differentiable manifolds, vectors on manifolds, tangent bundles, parallel transport and geodesics, tensors, metric structure, connections, Riemann curvature tensor.

Math 221A: Higher Algebra I

Prerequisites: Math 128B (Abstract Algebra II) or instructor consent.
Frequency: Alternating years (Fall, odd years)
Credit: 3 credits
Content: Topics from groups, rings, integral domains, modules, fields, vector spaces.
Subsequent Courses: Math 221B (Higher Algebra II)

Math 221B: Higher Algebra II

Prerequisites: Math 221A (Higher Algebra I)
Frequency: Alternating years (Spring, even years)
Credit: 3 credits
Recent Texts: (Jacobson, Hungerford, Grillet)
Background and Goals:
Content: Continuation of Math 221A with additional advanced topics in algebra selected by instructor.

Math 226: Theory of Numbers

Prerequisites: Math 126 (Theory of Numbers) and Math 128A (Abstract Algebra I) or instructor consent.
Frequency: Alternating years (Spring, odd years)
Credit: 3 credits
Recent Texts: A classical Introduction to Modern Number Theory (Ireland and Rosen), Elementary Number Theory and Its Applications (Pierre),
Content: Advanced topics in number theory selected by the instructor. Emphasis may be in algebraic number theory (e.g. Diophantine equations), analytic number theory (e.g. the prime number theorem), and/or computational number theory (e.g. cryptography).

Math 229: Advanced Matrix Theory

Prerequisites: Math 129B (Linear Algebra II) and an introduction to matrices such as Math 129A (Linear Algebra I).
Frequency: Alternating years (Fall, even years)
Credit: 3 credits
Recent Texts: Matrix Analysis (Horn and Johnson)
Background and Goals: To provide students with in-depth knowledge of basic research tools in matrix theory.
Content: Eigenvalues, unitary equivalence and Schur's theorem. Normal, Hermitian and symmetric real matrices. Positive definite matrices, polar and singular value factorizations, and selected topics at the discretion of the instructor.

Math 231A: Real Analysis I

Prerequisites: Math 131B (Introduction to Real Variables) or instructor consent.
Frequency: Alternating years (Spring, even years)
Credit: 3 credits
Recent Texts: The Elements of Integration and Lebesgue Measure (Bartle), Lebesgue Measure and Integrals (Craven and Pitman), Real analysis (Royden), Real and Complex Analysis (Rudin).
Background and Goals:
Content: This course includes the following topics: The concept of measurability, Lebesgue’s Monotone Convergence theorem, Fatou’s lemma, Lebesgue’s dominated convergence theorem, role played by sets of measure zero, Lebesgue measure, continuity properties of measureable functions, Borel sets, outer measure, measurable sets, convex functions, Lebesgue integral, integration of positive functions, L^p spaces, differentiation of measures.

Math 231B: Real Analysis II

Prerequisites: Math 231A (Real Analysis I)
Frequency: Alternating years (Fall, even years)
Credit: 3 credits
Recent Texts: Introductory Functional analysis with Applications (Kreyszig), Real and Complex Analysis (Rudin), Functional analysis, Volumes I and II (Kolomogorov and Fomin).
Background and Goals: A course in functional analysis.
Content: Normed linear spaces, Hilbert space and Banach spaces. The topics to be covered include: Metric spaces, Normed spaces, Banach spaces, Subspaces, Dual spaces, Compactness and completeness, Linear functionals, Riesz’ theorem, Hahn Banach theorem, Baire category theorem, open mapping theorem, closed graph theorem, Radon-Nikodym theorem, Linear operators, self-adjoint operators, unitary operators, Banach fixed point theorem .

Math 233A: Applied Mathematics I

Prerequisites: Math 133B (Partial Differential Equations)
Frequency: Alternating years (Spring, odd years)
Credit: 3 credits
Recent Texts: Partial differential equations of mathematical physics and integral equations (Guenther and Lee), An introduction to nonlinear partial differential equations (Logan).
Background and Goals: To cover the theory of the existence and uniqueness of solutions to first order systems of ordinary and partial differential equations. To introduce the elementary theory of function spaces including Banach and Hilbert spaces. To cover the theory of Fourier series and Fourier transforms. To discuss initial value-boundary value problems for the classical parabolic, hyperbolic and elliptic equations, and to give their solution by separation of variables. To present some basic types of nonlinear equation such as hyperbolic, diffusion and reaction-diffusion equations. To examine shock formation, weak solutions and travelling waves in representative equations derived from mathematical models taken from the literature.
Content: Derivation of the partial differential equations of classical mathematical physics. Existence and uniqueness of solutions of first order ordinary and partial differential equations. The classical theory of initial and boundary value problems for hyperbolic, parabolic and elliptic equations. Fourier series and transforms. Nonlinear partial differential equations.

Math 233B: Applied Mathematics II

Prerequisites: Math 138 (Complex Variables) and Math 233A (Applied Mathematics I)
Frequency: Alternating years (Fall, odd years)
Credit: 3 credits
Recent Texts: Perturbation Methods (Nayfeh), Partial differential equations of mathematical physics and integral equations (Guenther and Lee), An introduction to nonlinear partial differential equations (Logan).
Background and Goals: To enable students to be able to use perturbation theory in analysing ordinary and partial differential equations. To be able to solve general nonlinear first order partial differential equations by the method of characteristics. To cover the basic theory of Sobelev spaces for pdes. To present the mathematical theory behind the solution of the classical heat, wave and Laplace equations. To cover the theory of Fredholm and Volterrs integral equations.
Content: Continuation of Math 233A. Selected topics such as Green's functions, eigenvalue problems, integral equations, perturbation theory or variational methods.

Math 234: Advanced Dynamical Systems

Prerequisites: Math 134 (Dynamical Systems) or instructor consent.
Frequency: Alternating years (Fall, odd years).
Credit: 3 credits
Recent Texts: Introduction to Applied Nonlinear Dynamical Systems and Chaos (Wiggins).
Content: Continuous and discrete dynamical systems with applications. Topics include stability of equilibria and closed orbits, structural stability, applications in classical mechanics, biology and engineering, including control systems.

Math 235: Wavelets and their Applications

Prerequisites: Math 129A (Linear Algebra I) and Math 133B (Partial Differential Equations) or instructor's consent.
Frequency: Alternating years (Spring, odd years)
Credit: 3 credits
Recent Texts: An Introduction to Wavelet Analysis (Walnut)
Background and Goals: An elementary course in wavelets and their applications.
Content: Wavelets with particular emphasis on their use in the representation of digital signals and image analysis. Theory of filters, filter banks and wavelets with applications selected from image and video compression, speech, audio and ECG compression, and communication applications.

Math 238: Advanced Complex Variables

Prerequisites: Math 138 (Complex Variables) or instructor's consent.
Frequency: Alternating years (Fall, odd years)
Credit: 3 credits
Recent Texts: Complex Function Theory (Holland), Complex Analysis (Ahlfors), Invitation to Complex Analysis (Boas) Functions of One Complex Variables Volume I (Conway)
Background and Goals:
Content: A course specializing in one or more of the advanced branches of the theory of complex functions.

Math 243A: Advanced Numerical Analysis (Numerical Partial Differential Equations)

Prerequisites: Math 129A (Linear Algebra I), Math 143C or Math 143M (Numerical Analysis and Scientific Computing) or instructor consent.
Frequency: Alternating years (Fall, even years)
Credit: 3 credits.
Recent Texts: Numerical Solution of Partial Differential Equations (Smith)
Background and Goals: Many of the fundamental equations of physics, chemistry, engineering, economics and other areas are partial differential equations (PDE’s). In most applications the equations do not have convenient analytic solutions and numerical methods are required. In this course we discuss the finite difference method and also introduce the finite element method for solving the PDE’s. We look at elliptical, parabolic and hyperbolic equations. We discus ideas such as consistency, convergence, stability, iterative methods, sparse direct methods, characteristics and other ideas.
Content: Finite difference methods applied to parabolic, elliptic and hyperbolic equations including numerical methods for solving the discretized problem, convergence, stability, error control, and applications.

Math 243B: Advanced Topics in Numerical Analysis

Prerequisites: Math 143C or Math 143M (Numerical Analysis and Scientific Computing) or instructor consent.
Frequency: Alternating years (Spring, odd years)
Credit: 3 credits.
Recent Texts: Numerical Linear Algebra (Trefethen and Bau).
Background and Goals: To understand the commonly used algorithms for a selection topics. To be able to compare these algorithms in terms of efficiency, accuracy and reliability. To understand the derivations of the algorithms and the major theoretical results related to the algorithms, including their proofs. To develop the skills required to investigate a specific topic in depth and present the results of the investigation orally and in writing.
Content: Advanced topics in numerical methods.

Math 261A: Regression Theory and Methods

Prerequisites: Math 129A (Linear Algebra I) and either Math 161A (Applied Statistics I) or Math 164 (Mathematical Statistics).
Frequency: Alternating years (Fall, even years)
Credit: 3 credits
Content: Simple linear regression, multiple regression, indicator variables, influence diagnostics, transformations, assumption analysis, generalized linear models, nonlinear regression, CART, hypothesis testing, confidence and prediction intervals, variable selection and model building.

Math 261B: Design and Analysis of Experiments

Prerequisites: Math 261A (Regression Theory and Methods)
Frequency: Alternating years (Spring, odd years)
Credit: 3 credits.
Content: Principles, construction and analysis of experimental designs. ANOVA; randomized blocks, Latin squares, factorial, nested and other designs; fixed and random effects, multiple comparisons, repeated measures. Expected mean squares. Diagnostics and model comparison.

Math 265: Time Series Theory and Methods

Prerequisites: Math 129A (Linear Algebra I) and either Math 161A (Applied Statistics I) or Math 164 (Mathematical Statistics).
Frequency: Alternating years (Fall, odd years)
Credit: 3 credits
Recent Texts: Introduction to Time Series and Forecasting (Brockwell and Davis).
Content: Analysis of correlated data in time, trends, seasonal patterns, periodicity, autocorrelation, spectral/frequency analysis, filtering, ARIMA models, state-space models, forecasting. Applications from various fields including economics, signal processing, finance, atmospheric science.

Math 266: Survival Analysis and Reliability

Prerequisites: either Math 161A (Applied Statistics I) or Math 164 (Mathematical Statistics).
Frequency: Alternating years (Spring, even years)
Credit: 3 credits
Content: Statistical methods for analysis of time-to-event censored data. Survival distributions and hazard rates; Kaplan-Meier estimator; proportional hazards; partial likelihood; diagnostics. Applications from clinical trials, toxicology and tumorigenicity studies, epidemiological studies, and engineering reliability.

Math 271A: Mathematical Logic

Prerequisites: Math 171 (Foundations of Mathematics and Computer Science) or instructor's consent.
Frequency: Alternating years (Fall, odd years)
Credit: 3 credits
Recent Texts: A mathematical introduction to logic (Enderton).
Background and Goals: Develop the syntax and semantics of first-order logic. Prove the Completeness and Incompleteness
theorems and provide examples and applications.
Content: Formal systems; introductory model theory (Godel's completeness theorem, compactness, Lowenhein-Skolem theorem, etc.); Godel's incompleteness theorems.

Math 271B: Advanced Mathematical Logic

Prerequisites: Math 271A (Mathematical Logic) or instructor's consent.
Frequency: Alternating years (Spring, even years)
Credit: 3 credits
Recent Texts: Set Theory: An introduction to independence proofs (Kunen)
Background and Goals:
Content: A course specializing in one or more of the advanced branches of mathematical logic such as
set theory, recursion theory, proof theory, logic for computer science.

Math 275: Topology

Prerequisites: Math 175 (Topology) or instructor's consent.
Frequency: Alternating years (Spring, even years)
Credit: 3 credits
Content: A course specializing in one or more topics from advanced topology such as homotopy and the fundamental group, homology groups of spaces, continuum theory, function spaces, metrization, dimention theory, manifolds, topological groups.

Math 279A: Graph Theory

Prerequisites: Math 179 (Introduction to Graph Theory) or Math 142 (Introduction to Combinatorics) and an upper division algebra class, or instructor's consent.
Frequency: Alternating years (Spring, even years)
Credit: 3 credits
Recent Texts: Introduction to Graph Theory (West), Graphs and Digraphs (Chartrand and Lesniak).
Background and Goals:
Content: Advanced course in graph theory covering graphs, digraphs, trees, networks, connectedness, eulerian circuits, hamiltonian cycles, graph embeddings, matchings, factorizations, graph colorings and Ramsey theory.

Math 279B: Advanced Graph Theory

Prerequisites: Math 279A (Graph Theory)
Frequency: Alternating years (Fall, even years)
Credit: 3 credits
Content: Advanced topics in modern graph theory selected by instructor. Possible topics are algebraic graph theory, random graph theory, matroid theory, ramsey theory, expander graphs, and others.

Math 285: Advanced Topics in Mathematics

Prerequisites: Suitable upper division background in mathematics set by instructor.
Credit: 3 credits (repeatable for credit, up to a maximum of 12 credits)
Content: Selected topics in Mathematics. Topics vary each semester.

Math 298: Special Study

Prerequisites: Instructor's consent, approval of the graduate chair.
Credit: 1-4 credits (grading: Credit - No Credit, repeatable for credit)
Content: Advanced individual research and projects.

Math 299: Master's Thesis

Prerequisites: Admission to candidacy for the MA or MS degree, instructor's consent, approval of the graduate committee.
Credit: 1-4 credits (grading: Credit - No Credit, repeatable for credit)
Content: Advanced individual research and projects.

San Jose State University : Department of Mathematics

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